The Pythagorean Theorem states that in a right triangle, the sum of the areas of the squares on the two legs (sides A and B) is equal to the area of the square on the hypotenuse (side C). This can be expressed mathematically as:
\[ A^2 + B^2 = C^2 \]
Where:
- \( A \) and \( B \) are the lengths of the legs of the right triangle,
- \( C \) is the length of the hypotenuse.
Given the options you've presented:
- Option A states that the sum of the areas of squares B and C equals the area of square A. (Incorrect)
- Option B states that the sum of the areas of squares A and C equals the area of square B. (Incorrect)
- Option C states that the sum of the areas of squares A and B equals the area of square C. (Correct)
- Option D states that the difference of the areas of squares A and B is equal to the area of square C. (Incorrect)
Thus, the correct answer is:
C: The sum of the areas of squares A and B is equal to the area of square C.